Abstract

The increasing availability of spatio-temporal data has created new challenges for clustering geo-referenced time series, where both temporal dynamics and spatial structure play a crucial role. Traditional approaches typically focus on either temporal similarity or spatial proximity, often failing to capture the joint information contained in these two dimensions. This work introduces a new dissimilarity metric, the Bi-Gromov Dynamic Time Warping (Bi-GDTW) distance, intended to simultaneously address temporal alignment and spatial topology in geo-referenced time series. The proposed measure integrates the Gromov Dynamic Time Warping framework with the Gromov–Wasserstein distance, allowing temporal similarity to be modulated by the structural differences in the spatial configuration of the observed locations. We introduce a new Bi-Gromov K-means clustering algorithm that computes barycentric representatives of clusters in a joint spatio-temporal framework. The method enables the identification of clusters characterized by both similar temporal patterns and similar spatial structures. The performance of the proposed approach is evaluated through different simulation experiments. Results show that the Bi-GDTW-based clustering method outperforms approaches based exclusively on temporal or spatial information. In order to demonstrate the method's capacity to identify significant spatio-temporal clusters in environmental data, it is finally applied to daily temperature time series across Italian regions.